MEMS resonator
A micro-electromechanical resonator comprising a material having anisotropic directional elasticity characteristics. A shape of the resonator is such that a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge. This is true for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction.
1. A micro-electromechanical resonator comprising:
a material having anisotropic directional elasticity characteristics, wherein
a shape of the resonator is such that a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge, and
for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction.
2. The resonator of claim 1 , wherein
the shape is adapted in accordance with the directional characteristics to provide resonance in a predetermined extensional resonance mode,
the resonance mode producing an elastic deformation of the resonator which displaces the peripheral edge of the resonator, and
the displacement being substantially uniform at every point along a perimeter around the edge in the direction perpendicular to the edge at each point.
3. The resonator of claim 2 , wherein the predetermined extensional resonance mode is a quasi-longitudinal mode.
4. The resonator of claim 3 , wherein the shape is proportional to a slowness surface of the material, corresponding to the quasi-longitudinal mode.
5. The resonator of claim 1 , wherein the distance from the centroid to the peripheral edge is greatest and the modulus of elasticity is least in the direction of a crystal lattice of the resonator.
6. The resonator of claim 1 , further comprising a supporting stem attached to the centroid.
7. The resonator of claim 6 , wherein the resonator is biased by a bias voltage applied via the stem.
8. A micro-electromechanical system comprising:
a substrate;
an input electrode and an output electrode on the substrate; and
the micro-electromechanical resonator of claim 1 suspended above the substrate between the input and output electrodes.
9. The micro-electromechanical system of claim 8 , wherein the input and output electrodes are shaped so as to cooperate with the resonator to form an actuation gap between each electrode and the peripheral edge of the resonator, wherein
the gap is of a substantially uniform width at every point around the edge in the direction perpendicular to the edge at each point, and
the width is sufficient to accommodate displacement of the edge in a predetermined extensional resonance mode in which the resonator provides resonance, without the electrodes contacting the resonator.
10. A method of manufacturing a micro-electromechanical resonator, the resonator including a material having anisotropic directional elasticity characteristics, the method comprising:
selecting a shape of the resonator such that a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction; and
producing the resonator having the selected shape.
11. The method of claim 10 , wherein selecting a shape includes selecting a shape of the resonator to provide a predetermined quasi-longitudinal extensional resonance mode.
12. The method of claim 11 , wherein the step of selecting the shape comprises:
choosing a shape proportional to a slowness surface of the material, corresponding to the quasi-longitudinal mode.
13. A resonator apparatus comprising:
a first portion of a material having anisotropic directional elasticity characteristics, the first portion extending to a first point on a peripheral edge of the resonator apparatus that is a first distance in a first direction from a centroid of the resonator apparatus; and
a second portion of the material extending to a second different point on the peripheral edge that is a second distance in a second direction from the centroid, the first distance being greater than the second distance, the material having a lower modulus of elasticity in the first direction than in the second direction.
14. The apparatus of claim 13 , wherein the material is configured and arranged to exhibit uniform elastic expansion and contraction at the peripheral edge.
15. The apparatus of claim 13 , further including an anchor connected between the centroid and a substrate, the portions of the material not connected to the anchor being freely suspended over the substrate.